We propose a Generalized Uncertainty Principle (GUP) consistent with String Theory, Black Hole Physics and Doubly Special Relativity. This modifies all quantum mechanical Hamiltonians and predicts quantum gravity corrections. We compute corrections to the Lamb shift, simple harmonic oscillator, Landau levels, and the tunneling current. When applied to an elementary particle, it suggests that the space must be quantized, and that all measurable lengths are quantized in units of a fundamental length. We investigated whether GUP can explain the violation of the equivalence principle at small length scales that was observed experimentally. We investigated the consequences of GUP on Liouville theorem. We examined GUP effect on post inflation preheating, and show that it predicts an increase or a decrease in parametric resonance and a change in particle production. The effect of GUP on the creation of black holes is investigated to justify the experimental results from the Large Hadron Collider. / viii, 154 leaves ; 30 cm